Exponential form and logarithmic form, evaluating logarithms, and change of base

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Bo solves a math club card that asks for log₂ (1/8). What is log₂ (1/8)?

   -3
2. 2.

   Esme reads log 0.01 in a science book. What is log 0.01?

   -2
3. 3.

   Jun writes log₉ 3 on the class board. What is log₉ 3?

   1/2
4. 4.

   Kira writes log₂ (1/16) = -4 on a math club card. Which choice writes log₂ (1/16) = -4 as a power?

   • 2^(1/16) = -4
   • 2⁻⁴ = 1/16
   • (1/16)⁻⁴ = 2
   • (-4)² = 1/16
5. 5.

   Luz finds log₂₇ 3 = 1/3 in a math book. Which choice writes log₂₇ 3 = 1/3 as a power?

   • (1/3)²⁷ = 3
   • 27^(1/3) = 3
   • 27³ = 1/3
   • 3^(1/3) = 27

6. Read this first

   Growth table, × 2 on each arrow

   Row 0: 1; row 1: 2; row 2: 4; row 3: 8; row 4: 16; row 5: 32; row 6: 64.

7. 6.

   Noah looks for 20 in the × 2 growth table. log₂ 20 is between which two whole numbers?

   • 3 and 4
   • 1 and 2
   • 4 and 5
   • 5 and 6
8. 7.

   Row 0: 1; row 1: 3; row 2: 9; row 3: 27; row 4: 81. Pia looks for 50 in the × 3 growth table. log₃ 50 is between which two whole numbers?

   • 2 and 3
   • 4 and 5
   • 1 and 2
   • 3 and 4
9. 8.

   Row 0: 1; row 1: 5; row 2: 25; row 3: 125; row 4: 625. Ren looks for 300 in the × 5 growth table. log₅ 300 is between which two whole numbers?

   • 5 and 6
   • 4 and 5
   • 3 and 4
   • 2 and 3
10. 9.

    Tala finds log₃ 50 with a calculator, using log₃ 50 = log 50 ÷ log 3. To the nearest hundredth, what is log₃ 50?

    3.56
11. 10.

    Bo finds log₆ 90 with a calculator, using log₆ 90 = log 90 ÷ log 6. To the nearest hundredth, what is log₆ 90?

    2.51